Computing the Cassels–Tate pairing on the 3-Selmer group of an elliptic curve
2014 ◽
Vol 10
(07)
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pp. 1881-1907
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We extend the method of Cassels for computing the Cassels–Tate pairing on the 2-Selmer group of an elliptic curve, to the case of 3-Selmer groups. This requires significant modifications to both the local and global parts of the calculation. Our method is practical in sufficiently small examples, and can be used to improve the upper bound for the rank of an elliptic curve obtained by 3-descent.
1996 ◽
Vol 54
(2)
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pp. 267-274
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2015 ◽
Vol 11
(04)
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pp. 1233-1257
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2014 ◽
Vol 11
(01)
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pp. 269-297
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2014 ◽
Vol 17
(A)
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pp. 1-13
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2013 ◽
Vol 95
(2)
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pp. 189-200
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2009 ◽
Vol 148
(1)
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pp. 73-86
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2018 ◽
Vol 14
(05)
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pp. 1279-1304
2010 ◽
Vol 13
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pp. 451-460
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2011 ◽
Vol 151
(2)
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pp. 229-243
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